Also bidding for the showbiz “bible,” sources add, are Sharon Waxman’s site, the Wrap, and Jay Penske’s Penske Media — which owns Nikki Finke’s Deadline and Bonnie Fuller’s Hollywood Life.

Sources say that Burkle, Waxman and Penske have all been invited back to a “third round of bidding,” along with other potential buyers, for the 107-year-old Variety — and that the price is currently “in the upper $30 millions.”

The trade paper, being sold off by Reed Business Information, was estimated to be worth about $100 million in 2008, but The Post reported its valuation has since dipped sharply.

A source familiar with the offering explained the process whereby potential buyers give their pitches and are then “invited back” for each additional round of bidding.

“Ron owns other digital assets, so this is a smart move for him to be in that space,” said one media watcher. Others are wondering whether Burkle has a specific strategy in mind.

Waxman, meanwhile, has “an aggressive move up her sleeve,” the source said.

A rep for Burkle said, “I can’t comment on the speculation,” as did Waxman. Penske did not respond to requests for comment. Variety responded but would not comment.

Prometheus Media bought The Hollywood Reporter, a Variety rival, bundled with Billboard and other titles, from Nielsen in 2009 for $70 million. The company just replaced high-flying CEO Richard Beckman this week.